Polytope of Type {16,4,14}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,4,14}*1792b
if this polytope has a name.
Group : SmallGroup(1792,323449)
Rank : 4
Schlafli Type : {16,4,14}
Number of vertices, edges, etc : 16, 32, 28, 14
Order of s0s1s2s3 : 112
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,4,14}*896a
4-fold quotients : {4,4,14}*448, {8,2,14}*448
7-fold quotients : {16,4,2}*256b
8-fold quotients : {8,2,7}*224, {2,4,14}*224, {4,2,14}*224
14-fold quotients : {8,4,2}*128a
16-fold quotients : {4,2,7}*112, {2,2,14}*112
28-fold quotients : {4,4,2}*64, {8,2,2}*64
32-fold quotients : {2,2,7}*56
56-fold quotients : {2,4,2}*32, {4,2,2}*32
112-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
None in this atlas.
Irregular Quotients (of which this is a minimal cover):
None.
Permutation Representation (GAP) :
s0 := ( 1,449)( 2,450)( 3,451)( 4,452)( 5,453)( 6,454)( 7,455)( 8,456)( 9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)( 16,471)( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)( 24,465)( 25,466)( 26,467)( 27,468)( 28,469)( 29,484)( 30,485)( 31,486)( 32,487)( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)( 40,481)( 41,482)( 42,483)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 85,554)( 86,555)( 87,556)( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)(120,568)(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,582)(128,583)(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)(136,577)(137,578)(138,579)(139,580)(140,581)(141,596)(142,597)(143,598)(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)(153,594)(154,595)(155,603)(156,604)(157,605)(158,606)(159,607)(160,608)(161,609)(162,610)(163,611)(164,612)(165,613)(166,614)(167,615)(168,616)(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)(176,638)(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)(184,618)(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)(192,626)(193,627)(194,628)(195,629)(196,630)(197,666)(198,667)(199,668)(200,669)(201,670)(202,671)(203,672)(204,659)(205,660)(206,661)(207,662)(208,663)(209,664)(210,665)(211,652)(212,653)(213,654)(214,655)(215,656)(216,657)(217,658)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)(224,651)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)(249,690)(250,691)(251,692)(252,693)(253,708)(254,709)(255,710)(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)(265,706)(266,707)(267,715)(268,716)(269,717)(270,718)(271,719)(272,720)(273,721)(274,722)(275,723)(276,724)(277,725)(278,726)(279,727)(280,728)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)(305,739)(306,740)(307,741)(308,742)(309,778)(310,779)(311,780)(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,806)(352,807)(353,808)(354,809)(355,810)(356,811)(357,812)(358,799)(359,800)(360,801)(361,802)(362,803)(363,804)(364,805)(365,820)(366,821)(367,822)(368,823)(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)(376,817)(377,818)(378,819)(379,827)(380,828)(381,829)(382,830)(383,831)(384,832)(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)(392,840)(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)(400,862)(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)(408,842)(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)(416,850)(417,851)(418,852)(419,853)(420,854)(421,890)(422,891)(423,892)(424,893)(425,894)(426,895)(427,896)(428,883)(429,884)(430,885)(431,886)(432,887)(433,888)(434,889)(435,876)(436,877)(437,878)(438,879)(439,880)(440,881)(441,882)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)(448,875);;
s1 := ( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,274)(240,275)(241,276)(242,277)(243,278)(244,279)(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)(252,273)(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)(364,385)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,526)(464,527)(465,528)(466,529)(467,530)(468,531)(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)(476,525)(477,533)(478,534)(479,535)(480,536)(481,537)(482,538)(483,539)(484,540)(485,541)(486,542)(487,543)(488,544)(489,545)(490,546)(491,554)(492,555)(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)(500,549)(501,550)(502,551)(503,552)(504,553)(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,638)(576,639)(577,640)(578,641)(579,642)(580,643)(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)(588,637)(589,645)(590,646)(591,647)(592,648)(593,649)(594,650)(595,651)(596,652)(597,653)(598,654)(599,655)(600,656)(601,657)(602,658)(603,666)(604,667)(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)(612,661)(613,662)(614,663)(615,664)(616,665)(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)(680,757)(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,771)(688,772)(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)(696,780)(697,781)(698,782)(699,783)(700,784)(701,736)(702,737)(703,738)(704,739)(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)(712,733)(713,734)(714,735)(715,743)(716,744)(717,745)(718,746)(719,747)(720,748)(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)(728,756)(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)(792,869)(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,883)(800,884)(801,885)(802,886)(803,887)(804,888)(805,889)(806,890)(807,891)(808,892)(809,893)(810,894)(811,895)(812,896)(813,848)(814,849)(815,850)(816,851)(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)(824,845)(825,846)(826,847)(827,855)(828,856)(829,857)(830,858)(831,859)(832,860)(833,861)(834,862)(835,863)(836,864)(837,865)(838,866)(839,867)(840,868);;
s2 := ( 1,337)( 2,343)( 3,342)( 4,341)( 5,340)( 6,339)( 7,338)( 8,344)( 9,350)( 10,349)( 11,348)( 12,347)( 13,346)( 14,345)( 15,351)( 16,357)( 17,356)( 18,355)( 19,354)( 20,353)( 21,352)( 22,358)( 23,364)( 24,363)( 25,362)( 26,361)( 27,360)( 28,359)( 29,365)( 30,371)( 31,370)( 32,369)( 33,368)( 34,367)( 35,366)( 36,372)( 37,378)( 38,377)( 39,376)( 40,375)( 41,374)( 42,373)( 43,379)( 44,385)( 45,384)( 46,383)( 47,382)( 48,381)( 49,380)( 50,386)( 51,392)( 52,391)( 53,390)( 54,389)( 55,388)( 56,387)( 57,400)( 58,406)( 59,405)( 60,404)( 61,403)( 62,402)( 63,401)( 64,393)( 65,399)( 66,398)( 67,397)( 68,396)( 69,395)( 70,394)( 71,414)( 72,420)( 73,419)( 74,418)( 75,417)( 76,416)( 77,415)( 78,407)( 79,413)( 80,412)( 81,411)( 82,410)( 83,409)( 84,408)( 85,428)( 86,434)( 87,433)( 88,432)( 89,431)( 90,430)( 91,429)( 92,421)( 93,427)( 94,426)( 95,425)( 96,424)( 97,423)( 98,422)( 99,442)(100,448)(101,447)(102,446)(103,445)(104,444)(105,443)(106,435)(107,441)(108,440)(109,439)(110,438)(111,437)(112,436)(113,225)(114,231)(115,230)(116,229)(117,228)(118,227)(119,226)(120,232)(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,239)(128,245)(129,244)(130,243)(131,242)(132,241)(133,240)(134,246)(135,252)(136,251)(137,250)(138,249)(139,248)(140,247)(141,253)(142,259)(143,258)(144,257)(145,256)(146,255)(147,254)(148,260)(149,266)(150,265)(151,264)(152,263)(153,262)(154,261)(155,267)(156,273)(157,272)(158,271)(159,270)(160,269)(161,268)(162,274)(163,280)(164,279)(165,278)(166,277)(167,276)(168,275)(169,288)(170,294)(171,293)(172,292)(173,291)(174,290)(175,289)(176,281)(177,287)(178,286)(179,285)(180,284)(181,283)(182,282)(183,302)(184,308)(185,307)(186,306)(187,305)(188,304)(189,303)(190,295)(191,301)(192,300)(193,299)(194,298)(195,297)(196,296)(197,316)(198,322)(199,321)(200,320)(201,319)(202,318)(203,317)(204,309)(205,315)(206,314)(207,313)(208,312)(209,311)(210,310)(211,330)(212,336)(213,335)(214,334)(215,333)(216,332)(217,331)(218,323)(219,329)(220,328)(221,327)(222,326)(223,325)(224,324)(449,785)(450,791)(451,790)(452,789)(453,788)(454,787)(455,786)(456,792)(457,798)(458,797)(459,796)(460,795)(461,794)(462,793)(463,799)(464,805)(465,804)(466,803)(467,802)(468,801)(469,800)(470,806)(471,812)(472,811)(473,810)(474,809)(475,808)(476,807)(477,813)(478,819)(479,818)(480,817)(481,816)(482,815)(483,814)(484,820)(485,826)(486,825)(487,824)(488,823)(489,822)(490,821)(491,827)(492,833)(493,832)(494,831)(495,830)(496,829)(497,828)(498,834)(499,840)(500,839)(501,838)(502,837)(503,836)(504,835)(505,848)(506,854)(507,853)(508,852)(509,851)(510,850)(511,849)(512,841)(513,847)(514,846)(515,845)(516,844)(517,843)(518,842)(519,862)(520,868)(521,867)(522,866)(523,865)(524,864)(525,863)(526,855)(527,861)(528,860)(529,859)(530,858)(531,857)(532,856)(533,876)(534,882)(535,881)(536,880)(537,879)(538,878)(539,877)(540,869)(541,875)(542,874)(543,873)(544,872)(545,871)(546,870)(547,890)(548,896)(549,895)(550,894)(551,893)(552,892)(553,891)(554,883)(555,889)(556,888)(557,887)(558,886)(559,885)(560,884)(561,673)(562,679)(563,678)(564,677)(565,676)(566,675)(567,674)(568,680)(569,686)(570,685)(571,684)(572,683)(573,682)(574,681)(575,687)(576,693)(577,692)(578,691)(579,690)(580,689)(581,688)(582,694)(583,700)(584,699)(585,698)(586,697)(587,696)(588,695)(589,701)(590,707)(591,706)(592,705)(593,704)(594,703)(595,702)(596,708)(597,714)(598,713)(599,712)(600,711)(601,710)(602,709)(603,715)(604,721)(605,720)(606,719)(607,718)(608,717)(609,716)(610,722)(611,728)(612,727)(613,726)(614,725)(615,724)(616,723)(617,736)(618,742)(619,741)(620,740)(621,739)(622,738)(623,737)(624,729)(625,735)(626,734)(627,733)(628,732)(629,731)(630,730)(631,750)(632,756)(633,755)(634,754)(635,753)(636,752)(637,751)(638,743)(639,749)(640,748)(641,747)(642,746)(643,745)(644,744)(645,764)(646,770)(647,769)(648,768)(649,767)(650,766)(651,765)(652,757)(653,763)(654,762)(655,761)(656,760)(657,759)(658,758)(659,778)(660,784)(661,783)(662,782)(663,781)(664,780)(665,779)(666,771)(667,777)(668,776)(669,775)(670,774)(671,773)(672,772);;
s3 := ( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)( 88,202)( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)(288,401)(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)(296,407)(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)(304,420)(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)(312,426)(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)(320,432)(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)(328,438)(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)(336,444)(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)(456,569)(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)(464,575)(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)(496,606)(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)(504,612)(505,618)(506,617)(507,623)(508,622)(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)(516,628)(517,627)(518,626)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)(533,646)(534,645)(535,651)(536,650)(537,649)(538,648)(539,647)(540,653)(541,652)(542,658)(543,657)(544,656)(545,655)(546,654)(547,660)(548,659)(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)(556,672)(557,671)(558,670)(559,669)(560,668)(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)(680,793)(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)(688,799)(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)(696,812)(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)(704,818)(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)(712,824)(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)(720,830)(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)(728,836)(729,842)(730,841)(731,847)(732,846)(733,845)(734,844)(735,843)(736,849)(737,848)(738,854)(739,853)(740,852)(741,851)(742,850)(743,856)(744,855)(745,861)(746,860)(747,859)(748,858)(749,857)(750,863)(751,862)(752,868)(753,867)(754,866)(755,865)(756,864)(757,870)(758,869)(759,875)(760,874)(761,873)(762,872)(763,871)(764,877)(765,876)(766,882)(767,881)(768,880)(769,879)(770,878)(771,884)(772,883)(773,889)(774,888)(775,887)(776,886)(777,885)(778,891)(779,890)(780,896)(781,895)(782,894)(783,893)(784,892);;
poly := Group([s0,s1,s2,s3]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s3*s2, s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(896)!( 1,449)( 2,450)( 3,451)( 4,452)( 5,453)( 6,454)( 7,455)( 8,456)( 9,457)( 10,458)( 11,459)( 12,460)( 13,461)( 14,462)( 15,470)( 16,471)( 17,472)( 18,473)( 19,474)( 20,475)( 21,476)( 22,463)( 23,464)( 24,465)( 25,466)( 26,467)( 27,468)( 28,469)( 29,484)( 30,485)( 31,486)( 32,487)( 33,488)( 34,489)( 35,490)( 36,477)( 37,478)( 38,479)( 39,480)( 40,481)( 41,482)( 42,483)( 43,491)( 44,492)( 45,493)( 46,494)( 47,495)( 48,496)( 49,497)( 50,498)( 51,499)( 52,500)( 53,501)( 54,502)( 55,503)( 56,504)( 57,519)( 58,520)( 59,521)( 60,522)( 61,523)( 62,524)( 63,525)( 64,526)( 65,527)( 66,528)( 67,529)( 68,530)( 69,531)( 70,532)( 71,505)( 72,506)( 73,507)( 74,508)( 75,509)( 76,510)( 77,511)( 78,512)( 79,513)( 80,514)( 81,515)( 82,516)( 83,517)( 84,518)( 85,554)( 86,555)( 87,556)( 88,557)( 89,558)( 90,559)( 91,560)( 92,547)( 93,548)( 94,549)( 95,550)( 96,551)( 97,552)( 98,553)( 99,540)(100,541)(101,542)(102,543)(103,544)(104,545)(105,546)(106,533)(107,534)(108,535)(109,536)(110,537)(111,538)(112,539)(113,561)(114,562)(115,563)(116,564)(117,565)(118,566)(119,567)(120,568)(121,569)(122,570)(123,571)(124,572)(125,573)(126,574)(127,582)(128,583)(129,584)(130,585)(131,586)(132,587)(133,588)(134,575)(135,576)(136,577)(137,578)(138,579)(139,580)(140,581)(141,596)(142,597)(143,598)(144,599)(145,600)(146,601)(147,602)(148,589)(149,590)(150,591)(151,592)(152,593)(153,594)(154,595)(155,603)(156,604)(157,605)(158,606)(159,607)(160,608)(161,609)(162,610)(163,611)(164,612)(165,613)(166,614)(167,615)(168,616)(169,631)(170,632)(171,633)(172,634)(173,635)(174,636)(175,637)(176,638)(177,639)(178,640)(179,641)(180,642)(181,643)(182,644)(183,617)(184,618)(185,619)(186,620)(187,621)(188,622)(189,623)(190,624)(191,625)(192,626)(193,627)(194,628)(195,629)(196,630)(197,666)(198,667)(199,668)(200,669)(201,670)(202,671)(203,672)(204,659)(205,660)(206,661)(207,662)(208,663)(209,664)(210,665)(211,652)(212,653)(213,654)(214,655)(215,656)(216,657)(217,658)(218,645)(219,646)(220,647)(221,648)(222,649)(223,650)(224,651)(225,673)(226,674)(227,675)(228,676)(229,677)(230,678)(231,679)(232,680)(233,681)(234,682)(235,683)(236,684)(237,685)(238,686)(239,694)(240,695)(241,696)(242,697)(243,698)(244,699)(245,700)(246,687)(247,688)(248,689)(249,690)(250,691)(251,692)(252,693)(253,708)(254,709)(255,710)(256,711)(257,712)(258,713)(259,714)(260,701)(261,702)(262,703)(263,704)(264,705)(265,706)(266,707)(267,715)(268,716)(269,717)(270,718)(271,719)(272,720)(273,721)(274,722)(275,723)(276,724)(277,725)(278,726)(279,727)(280,728)(281,743)(282,744)(283,745)(284,746)(285,747)(286,748)(287,749)(288,750)(289,751)(290,752)(291,753)(292,754)(293,755)(294,756)(295,729)(296,730)(297,731)(298,732)(299,733)(300,734)(301,735)(302,736)(303,737)(304,738)(305,739)(306,740)(307,741)(308,742)(309,778)(310,779)(311,780)(312,781)(313,782)(314,783)(315,784)(316,771)(317,772)(318,773)(319,774)(320,775)(321,776)(322,777)(323,764)(324,765)(325,766)(326,767)(327,768)(328,769)(329,770)(330,757)(331,758)(332,759)(333,760)(334,761)(335,762)(336,763)(337,785)(338,786)(339,787)(340,788)(341,789)(342,790)(343,791)(344,792)(345,793)(346,794)(347,795)(348,796)(349,797)(350,798)(351,806)(352,807)(353,808)(354,809)(355,810)(356,811)(357,812)(358,799)(359,800)(360,801)(361,802)(362,803)(363,804)(364,805)(365,820)(366,821)(367,822)(368,823)(369,824)(370,825)(371,826)(372,813)(373,814)(374,815)(375,816)(376,817)(377,818)(378,819)(379,827)(380,828)(381,829)(382,830)(383,831)(384,832)(385,833)(386,834)(387,835)(388,836)(389,837)(390,838)(391,839)(392,840)(393,855)(394,856)(395,857)(396,858)(397,859)(398,860)(399,861)(400,862)(401,863)(402,864)(403,865)(404,866)(405,867)(406,868)(407,841)(408,842)(409,843)(410,844)(411,845)(412,846)(413,847)(414,848)(415,849)(416,850)(417,851)(418,852)(419,853)(420,854)(421,890)(422,891)(423,892)(424,893)(425,894)(426,895)(427,896)(428,883)(429,884)(430,885)(431,886)(432,887)(433,888)(434,889)(435,876)(436,877)(437,878)(438,879)(439,880)(440,881)(441,882)(442,869)(443,870)(444,871)(445,872)(446,873)(447,874)(448,875);
s1 := Sym(896)!( 15, 22)( 16, 23)( 17, 24)( 18, 25)( 19, 26)( 20, 27)( 21, 28)( 43, 50)( 44, 51)( 45, 52)( 46, 53)( 47, 54)( 48, 55)( 49, 56)( 57, 71)( 58, 72)( 59, 73)( 60, 74)( 61, 75)( 62, 76)( 63, 77)( 64, 78)( 65, 79)( 66, 80)( 67, 81)( 68, 82)( 69, 83)( 70, 84)( 85, 99)( 86,100)( 87,101)( 88,102)( 89,103)( 90,104)( 91,105)( 92,106)( 93,107)( 94,108)( 95,109)( 96,110)( 97,111)( 98,112)(127,134)(128,135)(129,136)(130,137)(131,138)(132,139)(133,140)(155,162)(156,163)(157,164)(158,165)(159,166)(160,167)(161,168)(169,183)(170,184)(171,185)(172,186)(173,187)(174,188)(175,189)(176,190)(177,191)(178,192)(179,193)(180,194)(181,195)(182,196)(197,211)(198,212)(199,213)(200,214)(201,215)(202,216)(203,217)(204,218)(205,219)(206,220)(207,221)(208,222)(209,223)(210,224)(225,253)(226,254)(227,255)(228,256)(229,257)(230,258)(231,259)(232,260)(233,261)(234,262)(235,263)(236,264)(237,265)(238,266)(239,274)(240,275)(241,276)(242,277)(243,278)(244,279)(245,280)(246,267)(247,268)(248,269)(249,270)(250,271)(251,272)(252,273)(281,323)(282,324)(283,325)(284,326)(285,327)(286,328)(287,329)(288,330)(289,331)(290,332)(291,333)(292,334)(293,335)(294,336)(295,309)(296,310)(297,311)(298,312)(299,313)(300,314)(301,315)(302,316)(303,317)(304,318)(305,319)(306,320)(307,321)(308,322)(337,365)(338,366)(339,367)(340,368)(341,369)(342,370)(343,371)(344,372)(345,373)(346,374)(347,375)(348,376)(349,377)(350,378)(351,386)(352,387)(353,388)(354,389)(355,390)(356,391)(357,392)(358,379)(359,380)(360,381)(361,382)(362,383)(363,384)(364,385)(393,435)(394,436)(395,437)(396,438)(397,439)(398,440)(399,441)(400,442)(401,443)(402,444)(403,445)(404,446)(405,447)(406,448)(407,421)(408,422)(409,423)(410,424)(411,425)(412,426)(413,427)(414,428)(415,429)(416,430)(417,431)(418,432)(419,433)(420,434)(449,505)(450,506)(451,507)(452,508)(453,509)(454,510)(455,511)(456,512)(457,513)(458,514)(459,515)(460,516)(461,517)(462,518)(463,526)(464,527)(465,528)(466,529)(467,530)(468,531)(469,532)(470,519)(471,520)(472,521)(473,522)(474,523)(475,524)(476,525)(477,533)(478,534)(479,535)(480,536)(481,537)(482,538)(483,539)(484,540)(485,541)(486,542)(487,543)(488,544)(489,545)(490,546)(491,554)(492,555)(493,556)(494,557)(495,558)(496,559)(497,560)(498,547)(499,548)(500,549)(501,550)(502,551)(503,552)(504,553)(561,617)(562,618)(563,619)(564,620)(565,621)(566,622)(567,623)(568,624)(569,625)(570,626)(571,627)(572,628)(573,629)(574,630)(575,638)(576,639)(577,640)(578,641)(579,642)(580,643)(581,644)(582,631)(583,632)(584,633)(585,634)(586,635)(587,636)(588,637)(589,645)(590,646)(591,647)(592,648)(593,649)(594,650)(595,651)(596,652)(597,653)(598,654)(599,655)(600,656)(601,657)(602,658)(603,666)(604,667)(605,668)(606,669)(607,670)(608,671)(609,672)(610,659)(611,660)(612,661)(613,662)(614,663)(615,664)(616,665)(673,764)(674,765)(675,766)(676,767)(677,768)(678,769)(679,770)(680,757)(681,758)(682,759)(683,760)(684,761)(685,762)(686,763)(687,771)(688,772)(689,773)(690,774)(691,775)(692,776)(693,777)(694,778)(695,779)(696,780)(697,781)(698,782)(699,783)(700,784)(701,736)(702,737)(703,738)(704,739)(705,740)(706,741)(707,742)(708,729)(709,730)(710,731)(711,732)(712,733)(713,734)(714,735)(715,743)(716,744)(717,745)(718,746)(719,747)(720,748)(721,749)(722,750)(723,751)(724,752)(725,753)(726,754)(727,755)(728,756)(785,876)(786,877)(787,878)(788,879)(789,880)(790,881)(791,882)(792,869)(793,870)(794,871)(795,872)(796,873)(797,874)(798,875)(799,883)(800,884)(801,885)(802,886)(803,887)(804,888)(805,889)(806,890)(807,891)(808,892)(809,893)(810,894)(811,895)(812,896)(813,848)(814,849)(815,850)(816,851)(817,852)(818,853)(819,854)(820,841)(821,842)(822,843)(823,844)(824,845)(825,846)(826,847)(827,855)(828,856)(829,857)(830,858)(831,859)(832,860)(833,861)(834,862)(835,863)(836,864)(837,865)(838,866)(839,867)(840,868);
s2 := Sym(896)!( 1,337)( 2,343)( 3,342)( 4,341)( 5,340)( 6,339)( 7,338)( 8,344)( 9,350)( 10,349)( 11,348)( 12,347)( 13,346)( 14,345)( 15,351)( 16,357)( 17,356)( 18,355)( 19,354)( 20,353)( 21,352)( 22,358)( 23,364)( 24,363)( 25,362)( 26,361)( 27,360)( 28,359)( 29,365)( 30,371)( 31,370)( 32,369)( 33,368)( 34,367)( 35,366)( 36,372)( 37,378)( 38,377)( 39,376)( 40,375)( 41,374)( 42,373)( 43,379)( 44,385)( 45,384)( 46,383)( 47,382)( 48,381)( 49,380)( 50,386)( 51,392)( 52,391)( 53,390)( 54,389)( 55,388)( 56,387)( 57,400)( 58,406)( 59,405)( 60,404)( 61,403)( 62,402)( 63,401)( 64,393)( 65,399)( 66,398)( 67,397)( 68,396)( 69,395)( 70,394)( 71,414)( 72,420)( 73,419)( 74,418)( 75,417)( 76,416)( 77,415)( 78,407)( 79,413)( 80,412)( 81,411)( 82,410)( 83,409)( 84,408)( 85,428)( 86,434)( 87,433)( 88,432)( 89,431)( 90,430)( 91,429)( 92,421)( 93,427)( 94,426)( 95,425)( 96,424)( 97,423)( 98,422)( 99,442)(100,448)(101,447)(102,446)(103,445)(104,444)(105,443)(106,435)(107,441)(108,440)(109,439)(110,438)(111,437)(112,436)(113,225)(114,231)(115,230)(116,229)(117,228)(118,227)(119,226)(120,232)(121,238)(122,237)(123,236)(124,235)(125,234)(126,233)(127,239)(128,245)(129,244)(130,243)(131,242)(132,241)(133,240)(134,246)(135,252)(136,251)(137,250)(138,249)(139,248)(140,247)(141,253)(142,259)(143,258)(144,257)(145,256)(146,255)(147,254)(148,260)(149,266)(150,265)(151,264)(152,263)(153,262)(154,261)(155,267)(156,273)(157,272)(158,271)(159,270)(160,269)(161,268)(162,274)(163,280)(164,279)(165,278)(166,277)(167,276)(168,275)(169,288)(170,294)(171,293)(172,292)(173,291)(174,290)(175,289)(176,281)(177,287)(178,286)(179,285)(180,284)(181,283)(182,282)(183,302)(184,308)(185,307)(186,306)(187,305)(188,304)(189,303)(190,295)(191,301)(192,300)(193,299)(194,298)(195,297)(196,296)(197,316)(198,322)(199,321)(200,320)(201,319)(202,318)(203,317)(204,309)(205,315)(206,314)(207,313)(208,312)(209,311)(210,310)(211,330)(212,336)(213,335)(214,334)(215,333)(216,332)(217,331)(218,323)(219,329)(220,328)(221,327)(222,326)(223,325)(224,324)(449,785)(450,791)(451,790)(452,789)(453,788)(454,787)(455,786)(456,792)(457,798)(458,797)(459,796)(460,795)(461,794)(462,793)(463,799)(464,805)(465,804)(466,803)(467,802)(468,801)(469,800)(470,806)(471,812)(472,811)(473,810)(474,809)(475,808)(476,807)(477,813)(478,819)(479,818)(480,817)(481,816)(482,815)(483,814)(484,820)(485,826)(486,825)(487,824)(488,823)(489,822)(490,821)(491,827)(492,833)(493,832)(494,831)(495,830)(496,829)(497,828)(498,834)(499,840)(500,839)(501,838)(502,837)(503,836)(504,835)(505,848)(506,854)(507,853)(508,852)(509,851)(510,850)(511,849)(512,841)(513,847)(514,846)(515,845)(516,844)(517,843)(518,842)(519,862)(520,868)(521,867)(522,866)(523,865)(524,864)(525,863)(526,855)(527,861)(528,860)(529,859)(530,858)(531,857)(532,856)(533,876)(534,882)(535,881)(536,880)(537,879)(538,878)(539,877)(540,869)(541,875)(542,874)(543,873)(544,872)(545,871)(546,870)(547,890)(548,896)(549,895)(550,894)(551,893)(552,892)(553,891)(554,883)(555,889)(556,888)(557,887)(558,886)(559,885)(560,884)(561,673)(562,679)(563,678)(564,677)(565,676)(566,675)(567,674)(568,680)(569,686)(570,685)(571,684)(572,683)(573,682)(574,681)(575,687)(576,693)(577,692)(578,691)(579,690)(580,689)(581,688)(582,694)(583,700)(584,699)(585,698)(586,697)(587,696)(588,695)(589,701)(590,707)(591,706)(592,705)(593,704)(594,703)(595,702)(596,708)(597,714)(598,713)(599,712)(600,711)(601,710)(602,709)(603,715)(604,721)(605,720)(606,719)(607,718)(608,717)(609,716)(610,722)(611,728)(612,727)(613,726)(614,725)(615,724)(616,723)(617,736)(618,742)(619,741)(620,740)(621,739)(622,738)(623,737)(624,729)(625,735)(626,734)(627,733)(628,732)(629,731)(630,730)(631,750)(632,756)(633,755)(634,754)(635,753)(636,752)(637,751)(638,743)(639,749)(640,748)(641,747)(642,746)(643,745)(644,744)(645,764)(646,770)(647,769)(648,768)(649,767)(650,766)(651,765)(652,757)(653,763)(654,762)(655,761)(656,760)(657,759)(658,758)(659,778)(660,784)(661,783)(662,782)(663,781)(664,780)(665,779)(666,771)(667,777)(668,776)(669,775)(670,774)(671,773)(672,772);
s3 := Sym(896)!( 1,114)( 2,113)( 3,119)( 4,118)( 5,117)( 6,116)( 7,115)( 8,121)( 9,120)( 10,126)( 11,125)( 12,124)( 13,123)( 14,122)( 15,128)( 16,127)( 17,133)( 18,132)( 19,131)( 20,130)( 21,129)( 22,135)( 23,134)( 24,140)( 25,139)( 26,138)( 27,137)( 28,136)( 29,142)( 30,141)( 31,147)( 32,146)( 33,145)( 34,144)( 35,143)( 36,149)( 37,148)( 38,154)( 39,153)( 40,152)( 41,151)( 42,150)( 43,156)( 44,155)( 45,161)( 46,160)( 47,159)( 48,158)( 49,157)( 50,163)( 51,162)( 52,168)( 53,167)( 54,166)( 55,165)( 56,164)( 57,170)( 58,169)( 59,175)( 60,174)( 61,173)( 62,172)( 63,171)( 64,177)( 65,176)( 66,182)( 67,181)( 68,180)( 69,179)( 70,178)( 71,184)( 72,183)( 73,189)( 74,188)( 75,187)( 76,186)( 77,185)( 78,191)( 79,190)( 80,196)( 81,195)( 82,194)( 83,193)( 84,192)( 85,198)( 86,197)( 87,203)( 88,202)( 89,201)( 90,200)( 91,199)( 92,205)( 93,204)( 94,210)( 95,209)( 96,208)( 97,207)( 98,206)( 99,212)(100,211)(101,217)(102,216)(103,215)(104,214)(105,213)(106,219)(107,218)(108,224)(109,223)(110,222)(111,221)(112,220)(225,338)(226,337)(227,343)(228,342)(229,341)(230,340)(231,339)(232,345)(233,344)(234,350)(235,349)(236,348)(237,347)(238,346)(239,352)(240,351)(241,357)(242,356)(243,355)(244,354)(245,353)(246,359)(247,358)(248,364)(249,363)(250,362)(251,361)(252,360)(253,366)(254,365)(255,371)(256,370)(257,369)(258,368)(259,367)(260,373)(261,372)(262,378)(263,377)(264,376)(265,375)(266,374)(267,380)(268,379)(269,385)(270,384)(271,383)(272,382)(273,381)(274,387)(275,386)(276,392)(277,391)(278,390)(279,389)(280,388)(281,394)(282,393)(283,399)(284,398)(285,397)(286,396)(287,395)(288,401)(289,400)(290,406)(291,405)(292,404)(293,403)(294,402)(295,408)(296,407)(297,413)(298,412)(299,411)(300,410)(301,409)(302,415)(303,414)(304,420)(305,419)(306,418)(307,417)(308,416)(309,422)(310,421)(311,427)(312,426)(313,425)(314,424)(315,423)(316,429)(317,428)(318,434)(319,433)(320,432)(321,431)(322,430)(323,436)(324,435)(325,441)(326,440)(327,439)(328,438)(329,437)(330,443)(331,442)(332,448)(333,447)(334,446)(335,445)(336,444)(449,562)(450,561)(451,567)(452,566)(453,565)(454,564)(455,563)(456,569)(457,568)(458,574)(459,573)(460,572)(461,571)(462,570)(463,576)(464,575)(465,581)(466,580)(467,579)(468,578)(469,577)(470,583)(471,582)(472,588)(473,587)(474,586)(475,585)(476,584)(477,590)(478,589)(479,595)(480,594)(481,593)(482,592)(483,591)(484,597)(485,596)(486,602)(487,601)(488,600)(489,599)(490,598)(491,604)(492,603)(493,609)(494,608)(495,607)(496,606)(497,605)(498,611)(499,610)(500,616)(501,615)(502,614)(503,613)(504,612)(505,618)(506,617)(507,623)(508,622)(509,621)(510,620)(511,619)(512,625)(513,624)(514,630)(515,629)(516,628)(517,627)(518,626)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)(533,646)(534,645)(535,651)(536,650)(537,649)(538,648)(539,647)(540,653)(541,652)(542,658)(543,657)(544,656)(545,655)(546,654)(547,660)(548,659)(549,665)(550,664)(551,663)(552,662)(553,661)(554,667)(555,666)(556,672)(557,671)(558,670)(559,669)(560,668)(673,786)(674,785)(675,791)(676,790)(677,789)(678,788)(679,787)(680,793)(681,792)(682,798)(683,797)(684,796)(685,795)(686,794)(687,800)(688,799)(689,805)(690,804)(691,803)(692,802)(693,801)(694,807)(695,806)(696,812)(697,811)(698,810)(699,809)(700,808)(701,814)(702,813)(703,819)(704,818)(705,817)(706,816)(707,815)(708,821)(709,820)(710,826)(711,825)(712,824)(713,823)(714,822)(715,828)(716,827)(717,833)(718,832)(719,831)(720,830)(721,829)(722,835)(723,834)(724,840)(725,839)(726,838)(727,837)(728,836)(729,842)(730,841)(731,847)(732,846)(733,845)(734,844)(735,843)(736,849)(737,848)(738,854)(739,853)(740,852)(741,851)(742,850)(743,856)(744,855)(745,861)(746,860)(747,859)(748,858)(749,857)(750,863)(751,862)(752,868)(753,867)(754,866)(755,865)(756,864)(757,870)(758,869)(759,875)(760,874)(761,873)(762,872)(763,871)(764,877)(765,876)(766,882)(767,881)(768,880)(769,879)(770,878)(771,884)(772,883)(773,889)(774,888)(775,887)(776,886)(777,885)(778,891)(779,890)(780,896)(781,895)(782,894)(783,893)(784,892);
poly := sub<Sym(896)|s0,s1,s2,s3>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2,
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2, s1*s2*s3*s2*s1*s2*s3*s2,
s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1,
s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
References : None.
to this polytope